Self-stabilizing Space Optimal Synchronization Algorithms on Trees

We present a space and (asymptotically) time optimal self-stabilizing algorithm for simultaneously activating non-adjacent processes in a rooted tree (Algorithm $\mathcal{SSDST}$). We then give two applications of the proposed algorithm: a time and space optimal solution to the local mutual exclusion problem (Algorithm $\mathcal{LMET}$) and a space and (asymptotically) time optimal distributed algorithm to place the values in min-heap order (Algorithm ${\mathcal{HEAP}}$). All algorithms are self-stabilizing and uniform, and they work under any unfair distributed daemon. In proving the time complexity of the heap construction, we use the notion of pseudo-time. Pseudo-time is similar to logical time introduced by Lamport [12]

[1]  Ronald L. Rivest,et al.  Introduction to Algorithms, Second Edition , 2001 .

[2]  Toshimitsu Masuzawa,et al.  Available stabilizing heaps , 2001, Inf. Process. Lett..

[3]  Ronald L. Rivest,et al.  Introduction to Algorithms , 1990 .

[4]  Anish Arora,et al.  Stabilization-Preserving Atomicity Refinement , 2002, J. Parallel Distributed Comput..

[5]  Ajoy Kumar Datta,et al.  Self-stabilizing neighborhood synchronizer in tree networks , 1999, Proceedings. 19th IEEE International Conference on Distributed Computing Systems (Cat. No.99CB37003).

[6]  Ajoy Kumar Datta,et al.  Snap-Stabilizing Optimal Binary Search Tree , 2005, Self-Stabilizing Systems.

[7]  Amos Israeli,et al.  Uniform Dynamic Self-Stabilizing Leader Election , 1997, IEEE Trans. Parallel Distributed Syst..

[8]  Yoshiaki Katayama,et al.  A self‐stabilizing max‐heap protocol in tree networks , 2003 .

[9]  Edsger W. Dijkstra,et al.  Self-stabilizing systems in spite of distributed control , 1974, CACM.

[10]  Ajoy Kumar Datta,et al.  State-optimal snap-stabilizing PIF in tree networks , 1999, Proceedings 19th IEEE International Conference on Distributed Computing Systems.

[11]  Ajoy Kumar Datta,et al.  Optimal Snap-Stabilizing Neighborhood Synchronizer in Tree Networks , 2002, Parallel Process. Lett..

[12]  Ajoy Kumar Datta,et al.  Self-stabilization with global rooted synchronizers , 1998, Proceedings. 18th International Conference on Distributed Computing Systems (Cat. No.98CB36183).

[13]  Leslie Lamport,et al.  Time, clocks, and the ordering of events in a distributed system , 1978, CACM.

[14]  Luc Onana Alima.  Self-stabilizing max-heap , 1999, Proceedings 19th IEEE International Conference on Distributed Computing Systems.

[15]  Clifford Stein,et al.  Introduction to Algorithms, 2nd edition. , 2001 .